Monolithic Microwave Integrated circuit (MMIC) chips operating at cryogenic temperatures have superconducting circuits that need to be thermally managed by removing the heat from the superconducting circuits down towards the substrate. Heat removal off the top side is inefficient due to superconducting solder bumps. This leads to unacceptably high temperature gradients. However, ground planes made of superconducting mesh material in lower level layers in the MMIC bring the entire layers to a thermal equilibrium. Because of this, portions of devices on the MMIC that need to be maintained at lower temperatures end up becoming exposed to higher temperature components. At the cryogenic conditions, heat load, cooling resources, and temperature are strongly tied to each other. The savings of one unit of power dissipation is magnified by multiple orders of magnitude when lifting from cryogenic temperatures to room temperature.
A typical superconducting electronic circuit will contain resistors made from a metal with a low electrical conductivity and superconducting elements that are fabricated in or on an insulating material. In typical operation, currents flowing through the resistors will generate heat in the form of hot electrons. The heat will be trapped in the electrons until it can convert to phonons via the electron-phonon coupling. The hot phonons will then travel through the circuit to the package and ultimately to the cryocooler. During their migration to the cryocooler, they heat the entire electronic circuit resulting in an increase in energy to maintain the electronic circuit at a desired operating temperature.